Wilcoxon signed-rank test of epsilon_N results vs. p_T

     Using the raw asymmetries from Jim Drachenberg's analysis of transverse single spin data with loose (0.1 - 0.2 GeV) and tight (0.105 - 0.165 GeV) invariant mass cuts, a comparison of the results was made using the Wilcoxon signed-rank test; see



This was done separately for x_F > 0 and x_F < 0 and 6 p_T bins from 5 - 6 GeV/c to 10 - 12 GeV/c.  The attached spreadsheet contains the individual raw asymmetries and calculations for the Wilcoxon test.  For x_F > 0, every one of the tight asymmetries is more positive than the corresponding loose asymmetry, and the sum of the signed ranks is 21, the maximum allowed for 6 pairs.  The first reference above suggests there is a 5% probability these two sets have the same median.

     For x_F < 0, the sum of the signed ranks is -3, and the probability is high that the two sets have the same median.

     Note for less than 6 pairs, there are no possible signed ranks that would indicate 5% probability or less that the two sets have the same median.  Thus, it makes no sense to test the data for x_F > 0 or x_F < 0 integrated over all p_T, since there would be only three pairs of asymmetries.